To solve for the additive inverse, you first need to understand what this concept means. The additive inverse of a number is what you need to add to that number to get zero. In other words, the additive inverse of [tex]\(a\)[/tex] is [tex]\(-a\)[/tex].
Given the complex number [tex]\(-8 + 3i\)[/tex], we follow these steps to find its additive inverse:
1. Identify the Real and Imaginary Parts:
The given complex number is [tex]\(-8 + 3i\)[/tex], where the real part is [tex]\(-8\)[/tex] and the imaginary part is [tex]\(3i\)[/tex].
2. Find the Additive Inverse:
- For the real part ([tex]\(-8\)[/tex]), the additive inverse is [tex]\(+8\)[/tex].
- For the imaginary part ([tex]\(3i\)[/tex]), the additive inverse is [tex]\(-3i\)[/tex].
Therefore, the additive inverse of [tex]\(-8 + 3i\)[/tex] is [tex]\(8 - 3i\)[/tex].
3. Convert the Additive Inverse Back to the List of Options:
We need to match [tex]\(8 - 3i\)[/tex] with the given options. The provided options are:
- [tex]\(-4 - 3\)[/tex]
- [tex]\(-4 + 3\)[/tex]
- [tex]\(3\)[/tex]
- [tex]\(8 + 3\)[/tex]
None of these options represent [tex]\(8 - 3i\)[/tex] directly. However, considering options that might have been listed incorrectly, we check the closest form:
- [tex]\(8 + 3i\)[/tex] is provided but the correct additive inverse is [tex]\(8 - 3i\)[/tex].
Since [tex]\(8 - 3i\)[/tex] is the correct additive inverse and closely related to the option [tex]\(8 + 3i\)[/tex], it seems like either a misprint or similarly close comprehension, but strictly speaking the correct form should be matched exactly.
So under the classical mathematical standard answer directly,
The additive inverse of [tex]\(-8 + 3i\)[/tex] is none other than [tex]\(8 - 3i\)[/tex], strictly checking for provided options retain closely invalid but logical interpretation as printable misunderstanding.
